This chapter reviews the theory of extremal quantile regression. It shows that each of the
sequences produces different asymptotic approximation to the distribution of the quantile …

This comprehensive text gives an interesting and useful blend of the mathematical,
probabilistic and statistical tools used in heavy-tail analysis. Heavy tails are characteristic of …

We consider quantile autoregression (QAR) models in which the autoregressive coefficients
can be expressed as monotone functions of a single, scalar random variable. The models …

Huge data sets from the teletraffic industry exhibit many nonstandard characteristics such as
heavy tails and long range dependence. Various estimation methods for heavy tailed time …

Because of its potential to... predict the unpredictable,... extreme value theory (EVT) and
methodology is currently receiving a great deal of attention from statistical and mathematical …

We consider a standard ARMA process of the form φ (B) Xt= θ (B) Zt, where the innovations
Zt belong to the domain of attraction of a stable law, so that neither the Zt nor the Xt have a …

Alexander McNeil's (1996) study of the Danish data on large fire insurance losses provides
an excellent example of the use of extreme value theory in an important application context …

Consider a sequence of possibly dependent random variables having the same marginal
distribution F, whose tail 1− F is regularly varying at infinity with an unknown index− α< 0 …

Extremal quantile regression, ie quantile regression applied to the tails of the conditional
distribution, counts with an increasing number of economic and financial applications such …

We consider a simple stationary bilinear model $ X_t= cX_ {t-1} Z_ {t-1}+ Z_t, t= 0,\pm 1,\pm
2,\dots, $ generated by heavy-tailed noise variables ${Z_t} $. A complete analysis of weak …